Gas-induced perturbations on the gravitational wave in-spiral of live post-Newtonian LISA massive black hole binaries

TL;DR

The paper addresses how gas in a circumbinary disk perturbs the gravitational-wave driven inspiral of an equal-mass MBHB in the LISA band. It employs 3D hydrodynamical simulations with a live binary and post-Newtonian dynamics up to $2.5$PN to capture the interplay between gas torques and GW emission, quantified by a dimensionless coupling parameter $\xi$. The authors measure a gas-induced orbital dephasing of $\delta \phi_{ m GW} \approx -0.014$ rad over $\sim278$ GW cycles, with contributions from orbital dephasing $\delta \phi_{ m orb}^{(GW)} = -0.007$ rad and precession dephasing $\delta \phi_{ m ecc}^{(GW)} = -0.012$ rad, implying detectability by LISA at redshift $z\sim1$ (SNR ~$1300$). This work demonstrates that GW observations can constrain the environment of MBHBs and informs future multi-messenger strategies, while highlighting limitations of PN and isothermal assumptions and outlining paths to more realistic physics.

Abstract

We investigate the effect of dynamically coupling gas torques with gravitational wave (GW) emission during the orbital evolution of an equal-mass massive black hole binary (MBHB). We perform hydrodynamical simulations of eccentric MBHBs with total mass $M=10^6~{\rm M}_\odot$ embedded in a prograde locally isothermal circumbinary disk (CBD). We evolve the binary from $55$ to $49$ Schwarzschild radii separations using up to 2.5 post-Newtonian (PN) corrections to the binary dynamics, which allow us to follow the GW-driven in-spiral. For the first time, we report the measurement of gas torques onto a live binary a few years before the merger, with and without concurrent GW radiation. We also report the gas-induced orbital dephasing $δφ_{\rm orb}\sim-0.007$ rad over $278$ orbital cycles that is likely driven mainly by disc-induced precession and LISA should be able to detect it at redshift $z=1$. Our results show how GWs alone can be used to probe the astrophysical properties of CBDs and have important implications for multi-messenger strategies aimed at studying the environments of MBHBs.

Figures (4)

• Figure 1: Column density ($\Sigma$) plots at three SMAs: $54.5~r_s$ (left panel), $52~r_s$ (middle panel), and $49.5~r_s$ (right panel) for the binary evolution under both GW and gas. Here $\Sigma$ varies between $\sim10^{3}$-$10^{7}$ g/cm$^{2}$. Both the binary (green dots) and the cavity shrink with time. Moreover, gas inflow inside the cavity creates short-lived mini-disks.
• Figure 2: Gas torques onto the binary in terms of $\xi$ as a function of the SMA for gas+PN2.5 simulation (light blue lines). We show average $\xi$ values for gas+PN2.5 (solid blue line; $\bar{\xi}_{\rm {gas+PN2.5}}\approx-19.5$) and gas+PN2 (dashed red line; $\bar{\xi}_{\rm gas+PN2}\approx-24.5$) cases, respectively. Note that we have not done any smoothing in plotting $\xi$ for the gas+PN2.5 run but only interpolation between snapshots.
• Figure 3: 2D projected gravitational torque ($T_{\rm grav}$) distribution between $-5a$ to $5a$ in both axes averaged over $100$ snapshots between $100^{\rm th}$ and $110^{\rm th}$ orbits. We show results from the gas+PN2.5 run (left panel), the gas+PN2 run (middle panel), and their difference (right panel). The third panel clearly shows that the gas+PN2.5 run has slightly more positive torque than the gas+PN2 simulation.
• Figure A1: Average torque value (blue cross) expressed in terms of $\bar{\xi}$ over initial 100 orbits of gas+PN2.5 simulations for three different resolutions: LR with $\Delta x[3a]={1.31~r_s}$, MR with $\Delta x[3a]={1.07~r_s}$, and HR with $\Delta x[3a]={0.66~r_s}$.